Eulerian Numbers

Author : T. Kyle Petersen
Publisher : Birkhäuser
ISBN 13 : 1493930915
Total Pages : 463 pages
Book Rating : 4.13/5 ( download)

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Download or read book Eulerian Numbers written by T. Kyle Petersen and published by Birkhäuser. This book was released on 2015-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.​

Author : J. Sándor
Publisher : Springer Science & Business Media
ISBN 13 : 1402025467
Total Pages : 637 pages
Book Rating : 4.64/5 ( download)

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Download or read book Handbook of Number Theory II written by J. Sándor and published by Springer Science & Business Media. This book was released on 2004 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.

Author : Robin Wilson
Publisher : Oxford University Press
ISBN 13 : 0192514067
Total Pages : 200 pages
Book Rating : 4.66/5 ( download)

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Download or read book Euler's Pioneering Equation written by Robin Wilson and published by Oxford University Press. This book was released on 2018-02-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Author : C. Edward Sandifer
Publisher : The Mathematical Association of America
ISBN 13 : 0883855844
Total Pages : 254 pages
Book Rating : 4.43/5 ( download)

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Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

Author : London Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 532 pages
Book Rating : 4.10/5 ( download)

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Download or read book Proceedings of the London Mathematical Society written by London Mathematical Society and published by . This book was released on 1900 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.72/5 ( download)

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Download or read book Proceedings written by and published by . This book was released on 1988 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 414 pages
Book Rating : 4.58/5 ( download)

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Download or read book The Quarterly Journal of Pure and Applied Mathematics written by and published by . This book was released on 1916 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sriram Pemmaraju
Publisher : Cambridge University Press
ISBN 13 : 9780521806862
Total Pages : 508 pages
Book Rating : 4.60/5 ( download)

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Download or read book Computational Discrete Mathematics written by Sriram Pemmaraju and published by Cambridge University Press. This book was released on 2003-12-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This definitive reference on Combinatorica contains examples of all 450 functions plus tutorial text.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author : Elena Deza
Publisher : World Scientific
ISBN 13 : 9814355488
Total Pages : 475 pages
Book Rating : 4.83/5 ( download)

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Download or read book Figurate Numbers written by Elena Deza and published by World Scientific. This book was released on 2012 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plane figurate numbers -- Space figurate numbers -- Multidimensional figurate members -- Areas of number theory including figurate numbers -- Fermat's polygonal number theorem.